Tuesday, November 7

Functions on Surfaces

There are many scattered data interpolation and approximation problems that arise on surfaces, for example, pressure or temperature on the Earth, or on the surface of an aircraft or other vehicle. Clearly it is vital to be able to represent these data. Most existing techniques are ad hoc or dependent on the choice of the coordinate system (e.g., the location of the poles on a sphere). Recent work generalized the planar Bernstein-Bezier Theory to the sphere and similar surfaces. This offers great potential for well founded and well understood new approximation and interpolation techniques. The speakers will survey previous work and discuss recent work, including their own. In particular, they will describe the application of Bernstein-Bezier technology on the sphere, reconstruction of scalar fields from scattered data, derivative and curvature properties of functions defined on surfaces, and the analogs of simplex splines on closed smooth surfaces.

Organizer: Peter W. Alfeld
University of Utah

10:30 A Bernstein-Bezier Theory on the Sphere and Similar Surfaces
Peter Alfeld, University of Utah; Larry Schumaker and Marian Neamtu, Vanderbilt University
11:00 Simplex Splines on the Sphere and on Other Closed Surfaces
Marian Neamtu, Vanderbilt University
11:30 C1 and C2 Reconstruction of Surfaces and Scalar Fields
Chandrajit Bajaj, F. Bernardini, J. Chen, and G. Xu, Purdue University
12:00 Construction and Visualization of Functions Defined on Surfaces
Helmut Pottmann and K. Opitz, Vienna Technical University, Austria

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